Theorem 3.2 (James [1]}) 
Suppose that \(1<p<\infty \) . Then for \(f(z)= \sum _{k=0}^{\infty } f_k z^k\)  and \(g(z)= \sum _{k=0}^{\infty } g_k z^k\)  belonging to \(\ell ^p_A\)  we have
\({f} \perp _{p} {g} \iff \sum _{k=0}^{\infty } |f_k|^{p - 2} \overline{f}_k g_k = 0,\) 
